• February 6, 2006—Northeastern Illinois University    
• March 10, 2006—Loyola University Chicago
• May 5, 2006—Saint Xavier University

Opening plenary session

New Vistas in Undergraduate Research: Partnerships with the National Science Foundation

Robert L. Kuczkowski, National Science Foundation (presenter), and Arthur B. Ellis, National Science Foundation

The growth of interdisciplinary research and the emergence of cyber tools are providing new paradigms in undergraduate research.  These developments offer the potential to reach a far broader cross-section of college students at an earlier stage of their college careers.  Examples of National Science Foundation-supported programs and projects will be presented for discussion. 

After dinner plenary session

The Summer Undergraduate Mathematical Science Research Institute (SUMSRI)

Dennis Davenport, Miami University

The Summer Undergraduate Mathematical Science Research Institute (SUMSRI) is a program conducted under the guidance of Miami University's Department of Mathematics and Statistics.  One of the goals of  SUMSRI is to prepare participants for the rigor and pace of graduate school.  The primary goal of the Institute is to provide approximately 15 nationally selected students with an intensive research experience augmented by formal and informal information sessions.  To accomplish these goals, SUMSRI runs seven weeks on Miami University's campus in Oxford, Ohio.  During these seven weeks, students participate in research seminars in mathematics or statistics. The program also includes a technical writing seminar, a GRE preparation workshop, two short courses on algebra and real analysis, and colloquium talks given by well known mathematical scientists.

Opening plenary session

Mapping the Domain of Mathematical Knowledge for Teaching: 

Knowing and Using Mathematics as a Teacher

Deborah Loewenberg Ball, University of Michigan, and Hyman Bass, University of Michigan

Although widespread agreement exists that content knowledge is essential for effective instruction, what is actually meant by "content knowledge" varies.   Terms such as "mathematical knowledge" and "pedagogical content knowledge" are used in different ways by different people, often without anyone noticing the confusion.  We suggest that efforts to design opportunities for teachers to learn mathematics are hampered by this lack of specification and discrimination, and the lack of shared definitions for terms and ideas about "content knowledge."  In this session, we will explore a set of distinctions that our research group has developed to "map" the territory of "mathematical knowledge for teaching" and consider what might be involved in helping teachers learn these different domains of content knowledge. 

After dinner plenary session

How I learned to Stop Worrying and Love NCLB -- Dr. Strangelove Redux?

James Pellegrino, University of Illinois at Chicago

At times the world of education seems as chaotic, absurd, and on the brink of self destruction as the world depicted in the classic 1964 movie Dr. Strangelove.  We have concerns about policies as well as the sanity of the persons behind them.  Such is the case today as educational leaders face the full onslaught of NCLB (No Child Left Behind).  But there is hope, for out of chaos can come order and beauty.  This presentation will explore how NCLB creates the context for a much more rational and useful discussion of the role of assessment in the educational system, and most especially, the ways in which assessment needs to be designed to support fundamental teaching and learning processes.  We will explore what contemporary research and theory about how students learn have to say about the design and use of assessment in the educational enterprise, and how NCLB creates the context for important changes in the status quo of educational testing and assessment.

March 10 Breakout Sessions

Scheduling of the breakout sessions is subject to change

Session 1        2:45 – 3:45 pm

How Well Do You Know Mathematics for Teaching?

Deborah Loewenberg, Ball, University of Michigan and Hyman Bass, University of Michigan

In this session, participants will examine further the research relating to the "mathematical knowledge for teaching" discussed in the plenary session.  Artifacts of practice, taken directly from the work of teaching mathematics, will be investigated by the participants.

Chicago Public Schools-University Course Partnership Program:  A first look at the first five years of quantitative teacher outcomes

Kelci Price, Chicago Public Schools, and Bret Feranchak, Chicago Public Schools

The Chicago Public Schools-University Course Partnership Program provides sequences of university courses to help in-service teachers deepen their mathematics and science content knowledge as well as earn their mathematics and/or science endorsements.  This session will focus on data about teachers’ participation in the Chicago Public Schools-University Course Partnership Program and the outcomes of the program, such as the numbers of teachers getting endorsement in mathematics and/or science and the rates at which teachers receive endorsements.  Over the last five years this program has involved 10 local universities and 1248 individual CPS teachers participating in over 240 classes with a total of 4100 course enrollments.  The session will involve an interactive presentation designed to engage the participants, presumed to represent various stakeholders’ perspectives, to reflect on and discuss their expectations for the endorsement programs sponsored by the CPS-University Course Partnership Program.  Following the discussion, we shall provide quantitative information about some of the outcomes of the program between 2001 and spring 2005, e.g., endorsements gained, number of courses taken by program, time taken to finish the endorsements, and retention and intensity rates.  The similarities and differences between expectations of the session participants and the data presented will be used as a launching point for further discussions.  Copies of the report on which the presentation is based will be distributed at the session.

Investigation of Teaching and Learning of Elementary School Mathematics Using “Math Trailblazers”

Susan Beal, University of Illinois at Chicago et al 

In our study of the teaching and learning of elementary school mathematics, we are investigating how teachers implement a curriculum, and to what extent the students in classes using Math Trailblazers are developing the concepts and operations that are the foci of the Math Trailblazers whole number strand.  Specifically, we will share our current findings from first grade classroom observations and student interviews.  Analysis of the observations provides information on how the teachers implement the literal lesson and the extent to which students have opportunities to reason about and communicate mathematics.  The analysis of the student interviews looks at students’ understanding of tens and ones, solving addition and subtraction word problems, and being able to read and use a graph.  Our goal is to connect students’ understandings to their experiences in Math Trailblazers classrooms.

Session 1I      4:15 – 5:15 pm

Beyond Rhetoric: Realities And Complexities Of Integrating Assessment Into Classroom Teaching And Learning

Jim Pellegrino, University of Illinois at Chicago 

Policy makers, educators, and the public are looking to assessments to serve a variety of purposes including gauging student learning, holding education systems accountable, signaling worthy goals for students and teachers to work toward, and providing useful feedback for instructional decision-making.  This session will focus on one critical component in building a comprehensive and coherent assessment system for mathematics within the Chicago Public Schools.  If assessment is to function well in support of the teaching and learning of mathematics it is essential that the district understand the assessment tools that are already available to its teachers, and the issues that surround their quality, utility, and implementation.  An overview will be provided about the types of assessments found within the CMSI’s (Chicago Math and Science Initiative) mathematics curricula and the quality and utility of those assessments based on detailed analyses of their properties.  Outcomes will be discussed in terms of three very important problems of practice.  Finally, we will set the results of our analysis of the curriculum-embedded assessments in the broader context of a system of assessments.  Here consideration is given to what such a system should look like and how it should function, including implications for professional development and technology tools and infrastructure.

Characteristics of Japanese Mathematics Lessons

Akihiko Takahashi, DePaul University 

Japanese mathematics lessons, especially for elementary grades, include a significant amount of problem solving.  This instructional approach, called structured problem-solving, is designed to create interest in mathematics and stimulate creative mathematical activity in the classroom through students’ collaborative work.  The lesson usually starts with students working individually to solve a problem using their own mathematical knowledge.  After working with problems, students bring various approaches and solutions to classroom discussion.  The teacher then leads students in a whole-class discussion in order to compare individual approaches and solutions.  This whole-class activity provides students with opportunities to develop their mathematical abilities including conceptual and procedural understanding.

By using the English translation of the most widely used Japanese mathematics textbook series (1-6), this session will describe notable characteristics of Japanese mathematics lessons.

Everyone’s a Critic:  An Example of Writing Assignments in Advanced Mathematics Courses

Reva Kasman, Grand Valley State University

Students in advanced, proof-based mathematics courses are expected to be able to analyze arguments for validity, particularly their own.  Despite our best efforts to teach proof-writing by example and provide explicit guidance, they are often overwhelmed by the challenge of choosing appropriate proof methods, writing coherent and logical arguments, and following conventions of style and notation.  In order to foster the development of these skills, I have been using a non-traditional type of writing assignment in these classes.  In each assignment, a mathematical problem is posed, and the students are provided with the solutions (including proof attempts) supposedly written by fictional characters.  The proofs are designed to illustrate certain misconceptions, difficult points, or typical writing flaws.  Students critique the work, categorize errors, and write short essays on their analysis.  Students, particularly future teachers, have responded positively to these assignments. 

During this breakout session, we will discuss the goals and structure of such an assignment, as well as the logistics of creating an ideal “wrong” solution or proof.  Participants will have the opportunity to examine some sample assignments from the perspective of a student, and then to work in small groups on the first stages of designing an original assignment. 

The mathematics in this session will be kept at a level suitable for a general mathematical audience.  Moreover, while some of the examples will involve proofs, the assignment format is easily adaptable for any mathematics course requiring critical thinking and analysis.

Advance announcement for the creation of the Illinois STEM Education Coalition

Gwen Pollock, Illinois State Board of Education

As state STEM education leaders, we are realizing the uncommon serendipity presented to us right now for action.  Many of us have heard calls for another Sputnik, another Nation at Risk; we are experiencing The World is Flat phenomenon.  The current impetus to realize the vital importance of the Illinois Science-Technology-Engineering-Mathematics (STEM) pipeline is building on national and international perspectives on economic competitiveness and progress.  Recent national reports from the Business Roundtable, the Business Higher Education Forum, the Council on Competitiveness, the National Academy of Sciences, the 2006 State of the Union address, and the PACE Congressional initiatives are coalescing the thinking and action at the federal, national, state, and regional and local levels.

This session will provide an overview of the revitalized Illinois Coalition for the STEM and STEM-Ed pipeline in Illinois in the context of

• the proposed strategies to identify the diversity of underlying causes of STEM challenges in Illinois and prepare to test correlating solutions to enhance the STEM pipeline in Illinois,
• the coalition’s purpose, which is to establish and sustain a coherent and comprehensive STEM pre-school to workforce pipeline for the new breed of educated and trained STEM workers and citizens who will productively contribute to the Illinois economy,
• the findings and recommendations in the about-to-be-released State of The State’s STEM-Education report, commissioned by the President of Northern Illinois University, Dr. John Peters. (as available for the symposium), and
• the possibilities to strategic planning and immediate, short and long-term action for biotechnology, manufacturing and engineering initiatives

May 5 Plenary Talks 

Opening plenary session

On Assessing Student Science Learning and Achievement

Richard J. Shavelson, Stanford University

Significant progress has been made in the assessment of student science learning and achievement.  This progress has been made both conceptually, with a cognitive model underlying what we mean by achievement, and procedurally, with a technology for assessing different aspects of achievement.  The conceptual model conceives science achievement as the acquisition of declarative (knowing that), procedural (knowing how), schematic (knowing why), and strategic (knowing when and where knowledge applies) knowledge, and the ability to reason along a learning trajectory.  This model provides the conceptual base for developing alternative tests of science achievement and learning.

The conceptual model combined with assessment technologies in a particular science-knowledge domain provides a basis for assessing science achievement.  While there is no one-to-one correspondence between test-item format and knowledge tapped, generally speaking declarative knowledge is most readily assessed by multiple-choice and short answer questions; the structure of this kind of knowledge can be assessed with concept maps.  Procedural knowledge can be assessed especially well with performance assessments.  Schematic knowledge can be assessed by a variety of formats including clusters of multiple-choice items, predict-observe-and-explain items, and open-ended items.  Schematic knowledge comes into play especially when students are challenged with new tasks, but students also use schematic knowledge when they are being assessed on the other knowledge types.  To be sure, the item format does not insure that the items tap the knowledge intended.  For this we turn to methods for validating interpretations of items and clusters of items that include cognitive analyses ("think aloud") and statistical analyses (e.g., confirmatory factor analysis). 

In this presentation, we shall discuss how the science assessment framework is applied in both large-scale summative assessment, namely the new framework for the Science Assessment in the National Assessment of Education Progress ("The Nation's Report Card"), and in formative assessment, namely a study of teachers' use of formative assessments embedded in science curriculum.
 

After dinner plenary session

Reforming the Preparation of Secondary Mathematics Teachers: An Innovative Four-Year Undergraduate Program

Alice Artzt, Queens College, CUNY, and Alan Sultan, Queens College, CUNY

We will describe an innovative model for preservice secondary mathematics teacher education, called TIME 2000 (i.e., Teaching Improvements through Mathematics Education).  This four-year undergraduate program was initially funded by the National Science Foundation in 1997, and has since become institutionalized at Queens College of the City University of New York.  Students are recruited directly from high school, are block scheduled into a coherent sequence of courses in mathematics and secondary education, and taught by a select group of professors.  Unlike traditional programs, students begin their involvement in schools and their study of educational psychology in the first semester of their freshman year.  Among the many innovative components of this program that will be described are monthly seminars, regular field trips, annual conferences, a student-run tutoring club, a monthly newsletter, and summer internships.  As well, excerpts from the monthly journals and annual portfolios that the students write documenting their experiences and their evolving knowledge and beliefs with regard to mathematics and mathematics teaching and learning will be shared.  We will also discuss the trials and tribulations associated with the collaboration between a mathematician with a content-driven perspective and a mathematics educator with a pedagogical perspective as they planned and implemented the calculus course for the TIME 2000 freshmen.

May 5 Breakout Sessions

SESSION I    2:45 – 3:45 pm 

On Formative Assessment

Richard Shavelson, Stanford University                                                                                                                         Room 103 

The focus of this session is on formative assessment practices.  Participants are engaged in an embedded assessment or “reflective lesson” aimed at eliciting their conceptual and schematic understanding of sinking and floating.  Techniques for using students’ (participants’) ideas elicited in the reflective lesson to build an argument to support one or another explanation will be enacted.  Participants will then take a topic of their own choosing and work through, briefly, the process of constructing their own reflective lessons beginning with specifying the outcome(s) of the topic and working backwards to students’ prior knowledge, and finding natural joints in the topic where formative assessments in the form of reflective lessons might be embedded.

History of Mathematics for Mathematics Majors

including preparation for pre-service secondary mathematics teachers

Margaret M. Bogacz, Saint Xavier University                                                                                                                         Room 102 

Students learn little of the origins of mathematics in their “regular” mathematics courses.  While they study the Pythagorean theorem, LaPlace transform, Fibonacci sequence, Cartesian coordinates, and Riemann sums, time rarely permits discussion of the fact that the right triangle relationship was known at least 1500 years before the time of Pythagoras, that Georg Riemann has also been credited with the discovery of elliptic geometry, or that Fibonacci introduced the Hindu-Arabic system of numeration to the Western world because he found it too cumbersome to do accounting using Roman numerals. 

An overview course in the history of mathematics provides math majors with the background necessary to understand the cultures, people, places, and theory of their major discipline.  Knowing the stories and anecdotes, ancient methods of arithmetic, algebra, and geometry can deepen their understanding and appreciation of the mathematics we know today.  Hearing of the successes and failures, hardships, achievements, and passions for learning and discovering of the men and women who created this discipline proves that mathematics is the product of human endeavor. 

How such a course has been developed and the variety of opportunities it creates will be discussed and illustrated.  Included in the course, besides the usual introduction typical of texts in the history of mathematics, is the reading of popular literature and viewing of modern films which have mathematics related themes.  Examples of these are plays (Proof and Arcadia), novels (Uncle Petros and the Goldbach Conjecture  and The French Mathematician), biographies (The Man Who Loved Only Numbers and Women in Mathematics) and movies (A Beautiful Mind and Pi). 

After a 30-35 minute presentation giving an overview of the typical content of the first week of the course, the presenter will lead a discussion on other approaches to teaching a history of mathematics course for math majors. 

Lists of books and videos used in the course, highlights of the course syllabus, and list of texts will be distributed.

One-on-One Math Tutoring as a Freshman Preservice Clinical Experience

Diane Profita Schiller, Loyola University Chicago                                                                                                                         Room 104 

Tutoring is a powerful experience for preservice teachers.  During Math for Elementary School Teachers I at Loyola University Chicago, candidates develop 6 point lesson plans for a one hour tutoring session from 7:30-8:30 am at Swift School.  Loyola undergraduates are assigned a middle school student with whom they work for 12 weeks.  Each lesson includes a greeting, a computer activity, an interesting problem or riddle, a game, an extended ISAT problem, and review of math homework.  Upon completing each lesson, candidates assess student achievement and reflect upon their own performance.  This semester-long program meets a core requirement for civic engagement in the Loyola University Chicago undergraduate program. 

Tutoring is facilitated through the COUNTDOWN web site.  In preparing lessons, tutors view quick time movies to see how teachers taught the lesson and how students responded to the instruction. 

Following a short presentation of the web site and data on tutor and student performance, the session will be devoted to a participant discussion focused on four areas:

• the value of one-on-one tutoring experience for the teacher preparation undergraduate;
• cost-effective models for preparing students to tutor;
• the value of tutoring to the middle school student; and
• the integration of classroom instruction and tutoring.

Participants will receive a copy of the lesson plan frame, ISAT extended response, and information about the free COUNTDOWN web site.
 

2:45 – 5:15 pm

Workshop on 

Teaching Discrete Mathematics to K-8 Teachers

Presenter:

Bonnie Saunders, University of Illinois at Chicago 

Room 101 

The workshop will explore the new book, Discrete Mathematics for K-8 Teachers by Valerie DeBellis, Shodor Education Foundation, and Joseph Rosenstein, Rutgers University. By covering topics from graph theory, in-depth and appropriately for K-8 teachers, the lessons in this book make mathematical concepts come alive for students while improving reasoning and problem-solving skills.  The book is interactive with three different sections:  written discussion with problems, activities, and K-8 classroom guides.  Samples of all three sections will be distributed at the workshop. 

The workshop will consist of a series of activities, designed to introduce participants to the extent of the material covered in the book and the many ways the materials involve students in problem solving and mathematical discourse.  Discussion of each activity will include: the how and why of the mathematics; examples of teachers’ work; and related K-8 classroom activities. 

Note about participation:

If you have not registered in advance, please check with Bonnie Saunders about available spaces.
 

SESSION II       4:15 – 5:15 pm 

Shaping Our Future Teachers- Novel Courses in Educational Psychology and Mathematics

Alice Artzt, Queens College CUNY, and Alan Sultan, Queens College CUNY                                                                                                                         Room 103 

This session focuses on two innovative courses that were developed as part of the TIME 2000 Program.  First a description will be given of a first-semester freshman-level course in the psychology of learning mathematics.  Students use their experiences in their college calculus course as the context for self-reflection and study of how they and others learn mathematics.  To examine how the psychological theories they learn are used by school teachers and their students, they participate in lesson-study type activities during a structured fieldwork experience supervised by a TIME 2000 professor.   

The second part of this session, will describe an innovative mathematics course in which college juniors engage in experiences designed to enable them to gain a deeper understanding and enjoyment of the mathematics they will be teaching.  Students in this class work in small groups to plan and conduct five class sessions that address one of the following content strands from the secondary school curriculum:  Algebra, Geometry, Measurement, Data Analysis, and Probability.  The students examine the historical development of the topics, the way the topics are developed in the k-12 curriculum, and the higher-level concepts that underlie the topics.  Students create and engage their classmates in problem-solving activities that best highlight these ideas in secondary school, usually incorporating the use of manipulatives, computers, graphing calculators, and calculator-based laboratories.  They design and assign homework, create and administer quizzes, and engage in group assessment of their classmates’ work.  At the conclusion of their presentation, students in each group submit a portfolio documenting their work, including their personal reflections on the experience.  We will share the individual and group-made portfolios constructed by students in these classes.

Integrating Technology into Mathematics and Mathematics Education

Michael Hardy, Saint Xavier University

Room 102

To introduce the discussion on methods of teaching mathematics courses and mathematics methods courses using technology, the discussion facilitator will present a brief description of some pre-service elementary teachers’ impressions of the extent to which their professors taught with technology, followed by a quick demonstration of some methods of using technology that the session facilitator employs, or endorses, and a discussion of the merits of these methods.  After the 15-minute introduction, the rest of the session will be a round table discussion. 

Participants will be invited to discuss how and why they use technology in their teaching.  Attention will also be devoted to discussing participants’ perceptions of the need for and problems associated with integrating the use of technology into mathematics and mathematics education courses, as well as potential solutions to these problems.  The discussion facilitator will pose questions initially and as needed, but questions for discussion will primarily be sought from the participants. 

Participants will receive hard copies of the activities or diagrams associated with the facilitator’s presentation.  Electronic copies will also be made available via email.

Distance Learning Courses in the Natural Sciences

Dana Perry, Harold Washington College, Dennis Lehman, Harold Washington College, Joel Tassin, Harold Washington College, and Brandon Taylor, City Colleges of Chicago

Room 104 

This session focuses on distance learning in the natural sciences.  The City Colleges of Chicago has a successful Center for Distance Learning (CDL) that offers distance learning college credit courses annually over three semesters, Spring, Summer, and Fall, serving over 9,000 students across the seven campuses of the City Colleges.  Over 100 faculty, both full time and adjunct, teach the courses.  During this breakout session, Brandon Taylor will provide an overview of the CDL, including an explanation of TW courses, the Student Readiness Quiz, and the Faculty Academy. 

TeleWeb courses (TW) are offered in an 8 week session for summer and 16 weeks for Spring and Fall.  These courses combine Internet-based instruction with video.  Students gain access to the video by watching the programs on WYCC-TV/Channel 20 or renting the videocassettes. 

Several natural science courses are offered through CDL, including astronomy, geology, and physical sciences.  Dennis Lehman developed and teaches the distance learning Physical Science 107 TW course, and Joel Tassin created and teaches the Geology 201 TW course that includes a laboratory component.  Each presenter will discuss the development and implementation of their courses, demonstrating the use of Discussion Boards, Assignments, Exams, and Laboratories in Blackboard, in addition to the specific video component of the courses. 

The presenters will project the Blackboard sites of their distance learning courses, allowing participants to engage in the discussion of the course components.  Relevant handouts may be provided.